{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Lagrangian Neural Networks\n",
    "\n",
    "In this tutorial we take a look at **Lagrangian Nets** (LNNs) first proposed in [Lutter M., et al, 2019](https://arxiv.org/abs/1907.04490) and generalized by [Cranmer M., et al., 2020](https://arxiv.org/abs/2003.04630). Together with HNNs [Greydanus S., et al., 2019](https://arxiv.org/abs/1906.01563), LNNs represent the latest learning paradigm to discover symmetries and conservation laws from data.\n",
    "\n",
    "Let $\\mathcal{Q}\\subset\\mathbb{R}^n$ be a smooth manifold anf let $q\\in\\mathcal{Q}$ be a vector of generalized coordinates. The Lagrangian function $\\mathcal{L}:\\mathcal{TQ}\\rightarrow\\mathbb{R}$ is defined on the tangent bundle $\\mathcal{TQ}$ of the configuration manifold $\\mathcal{Q}$ (if $\\mathcal{Q}=\\mathbb{R}^n$, then $\\mathcal{TQ}$ is diffeomorphic to $\\mathbb{R}^{2n}$), i.e. the Lagrangian is a function of the configurations $q$ and their velocities $\\dot q$.\n",
    "\n",
    "Derived from the calculus of variations, the Euler-Lagrange equations of motions can be generally explicitly written as a second-order ordinary differential equation:\n",
    "\n",
    "$$\n",
    "    \\ddot q = \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}\\right)^{-1}\\left[\\nabla_q\\mathcal{L} - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L\\right)\\dot q\\right]\n",
    "$$\n",
    "\n",
    "**Lagrangian Neural Networks** try to mimick Euler-Lagrange equations by learning from data a Lagrangian $\\mathcal{L}_\\theta$ parametriezed by a *neural network* (with parameters $\\theta$). \n",
    "\n",
    "When a net of tuples $\\{(q_k,\\dot q_k, \\ddot q_k)\\}_{k=1,\\dots,K}$ generated by some conservative dynamical process is available, LNNs are trained to learn the Lagrangian from the data by minimizing, e.g. the *MSE loss*:\n",
    "$$\n",
    "    \\min_{\\theta}\\frac{1}{K}\\sum_{k=1}^K\\left\\|\\ddot q_k - \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}_\\theta(q_k, \\dot q_k)\\right)^{-1}\\left[\\nabla_q\\mathcal{L}_\\theta(q_k, \\dot q_k) - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L_\\theta(q_k, \\dot q_k)\\right)\\dot q_k\\right]\\right\\|_2^2\n",
    "$$\n",
    "\n",
    "\n",
    "We hereby showcase the torchdyn implementation of LNNs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import sys\n",
    "sys.path.append('../')\n",
    "from torchdyn.models import *; from torchdyn.datasets import *\n",
    "from torchdyn import *"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The vector field of an LNN, to be passed to a `NeuralDE` can be defined as:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from torch.autograd.functional import jacobian, hessian ; from functools import partial\n",
    "\n",
    "class LNN(nn.Module):\n",
    "    def __init__(self, net):\n",
    "        super().__init__()\n",
    "        self.net = net\n",
    "    def forward(self, x):\n",
    "        self.n = n = x.shape[1]//2 ; bs = x.shape[0]   \n",
    "        x = torch.autograd.Variable(x, requires_grad=True)\n",
    "        qqd_batch = tuple(x[i, :] for i in range(bs))\n",
    "        jac = tuple(map(partial(jacobian, self._lagrangian, create_graph=True), qqd_batch))\n",
    "        hess = tuple(map(partial(hessian, self._lagrangian, create_graph=True), qqd_batch))\n",
    "        qdd_batch = tuple(map(self._qdd, zip(jac, hess, qqd_batch)))\n",
    "        qd, qdd = x[:, n:], torch.cat([qdd[None] for qdd in qdd_batch])\n",
    "        return torch.cat([qd, qdd], 1)\n",
    "    \n",
    "    def _lagrangian(self, qqd):\n",
    "        return self.net(qqd).sum()\n",
    "    \n",
    "    def _qdd(self, inp):\n",
    "        n = self.n ; jac, hess, qqd = inp\n",
    "        return hess[n:, n:].pinverse()@(jac[:n] - hess[n:, :n]@qqd[n:])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We consider a 1D mass-spring system\n",
    "\n",
    "$$\n",
    "    m\\ddot x + kx = 0,~~~[x(0),\\dot x(0)]\\sim \\mathcal N(0,I)\n",
    "$$\n",
    "\n",
    "Following the LNN paper from Cranmer et al., we generate random values of $x,\\dot x$ and we fit (in a static manner) the corresponding $\\ddot q$."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## \"Static\" Training"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "m, k, l, g = 1, 1, 1, 9.81\n",
    "X = torch.randn(4096,2).to(device)\n",
    "Xdd = -k*X[:,0]/m\n",
    "\n",
    "train = data.TensorDataset(X, Xdd)\n",
    "trainloader = data.DataLoader(train, batch_size=32, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model.defunc(0, x)\n",
    "    \n",
    "    def loss(self, y_hat, y):\n",
    "        return ((y - y_hat[:,1])**2).mean()\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x, y = batch\n",
    "        y_hat = self.model.defunc(0, x) #static training: we do not solve the ODE \n",
    "        loss = self.loss(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "hdim = 128\n",
    "net = LNN(nn.Sequential(\n",
    "            nn.Linear(2,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,1))\n",
    "         ).to(device)\n",
    "\n",
    "model = NeuralDE(func=net, solver='dopri5').to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 17 K  \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "d391be985284431e9a8579170a6de2a1",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=1, max_epochs=2)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NFE: 20\n",
      "inference time: 48.30189228057861\n",
      "avg time per function evaluation: 2.4150946140289307\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the training results\n",
    "import time\n",
    "t = time.time()\n",
    "model.nfe = 0\n",
    "X0 = torch.Tensor(256, 2).uniform_(-1,1).to(device)\n",
    "s_span = torch.linspace(0, 1, 100)\n",
    "traj = model.trajectory(X0, s_span).cpu().detach()\n",
    "T = time.time() - t\n",
    "print(f\"NFE: {model.nfe}\\ninference time: {T}\\navg time per function evaluation: {T/model.nfe}\")\n",
    "# the inference time to compute a full trajectory is currently still quite high \n",
    "# and scales with the batch. We are aware of this issue and we will release \n",
    "# an accellerated version soon "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"LNN's learned trajectories\")"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the LNN's trajectories with random ICs\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "color = ['orange', 'blue']\n",
    "for i in range(len(X0)):\n",
    "    ax.plot(traj[:,i,0], traj[:,i,1], color='blue', alpha=0.1);\n",
    "ax.set_xlim([-1,1])\n",
    "ax.set_ylim([-1,1])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"LNN's learned trajectories\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Lagrangian & Vector Field')"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Lagrangian and learned vector field\n",
    "n_grid =  50\n",
    "x = torch.linspace(-1,1,n_grid)\n",
    "Q, P = torch.meshgrid(x,x)\n",
    "H, U, V = torch.zeros(Q.shape), torch.zeros(Q.shape), torch.zeros(Q.shape)\n",
    "for i in range(n_grid):\n",
    "    for j in range(n_grid):\n",
    "        x = torch.cat([Q[i,j].reshape(1,1),P[i,j].reshape(1,1)],1).to(device)\n",
    "        H[i,j] = model.defunc.m.net(x).detach().cpu()\n",
    "        O = model.defunc(0,x).detach().cpu()\n",
    "        U[i,j], V[i,j] = O[0,0], O[0,1]\n",
    "        \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q,P,H,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),P.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([P.min(),P.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"Learned Lagrangian & Vector Field\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Forced Lagrangian\n",
    "\n",
    "Can we easily extend the framework to the non-conservative case where some forcing term is present?\n",
    "\n",
    "Yes of course!\n",
    "\n",
    "We can add a learnable forcinf term $f(q,\\dot q)$ to the system obtaining:\n",
    "\n",
    "$$\n",
    "    \\ddot q = \\left(\\nabla_{\\dot q} \\nabla_{\\dot q}^\\top \\mathcal{L}\\right)^{-1}\\left[\\nabla_q\\mathcal{L} - \\left(\\nabla_q\\nabla^\\top_{\\dot q}\\mathcal L\\right)\\dot q + f(q, \\dot q)\\right]\n",
    "$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "class fLNN(nn.Module):\n",
    "    def __init__(self, L, f):\n",
    "        super().__init__()\n",
    "        self.L = L\n",
    "        self.f = f\n",
    "    def forward(self, x):\n",
    "        self.n = n = x.shape[1]//2 ; bs = x.shape[0]    \n",
    "        x = torch.autograd.Variable(x, requires_grad=True)\n",
    "        qqd_batch = tuple(x[i, :] for i in range(bs))\n",
    "        jac = tuple(map(partial(jacobian, self._lagrangian, create_graph=True), qqd_batch))\n",
    "        hess = tuple(map(partial(hessian, self._lagrangian, create_graph=True), qqd_batch))\n",
    "        qdd_batch = tuple(map(self._qdd, zip(jac, hess, qqd_batch)))\n",
    "        qd, qdd = x[:, n:], torch.cat([qdd[None] for qdd in qdd_batch])\n",
    "        return torch.cat([qd, qdd], 1)\n",
    "    \n",
    "    def _lagrangian(self, qqd):\n",
    "        return L(qqd).sum()\n",
    "    \n",
    "    def _qdd(self, inp):\n",
    "        n = self.n ; jac, hess, qqd = inp\n",
    "        return hess[n:, n:].pinverse()@(jac[:n] - hess[n:, :n]@qqd[n:] + self.f(qqd))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We now consider, e.g., a 1D mass-spring-damper system \n",
    "\n",
    "$$\n",
    "    m\\ddot x + kx + b\\dot x = 0,~~~[x(0),\\dot x(0)]\\sim \\mathcal N(0,I)\n",
    "$$\n",
    "\n",
    "and we let $q=x$, $p=\\dot x$. We then train the neural network on random generated data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch.utils.data as data\n",
    "device = torch.device(\"cuda:0\" if torch.cuda.is_available() else \"cpu\")\n",
    "\n",
    "m, k, b = 1, 1, 1\n",
    "X = torch.randn(4096,2).to(device)\n",
    "Xdd = -k*X[:,0]/m - b*X[:,1]/m\n",
    "\n",
    "train = data.TensorDataset(X, Xdd)\n",
    "trainloader = data.DataLoader(train, batch_size=32, shuffle=False)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pytorch_lightning as pl\n",
    "\n",
    "class Learner(pl.LightningModule):\n",
    "    def __init__(self, model:nn.Module):\n",
    "        super().__init__()\n",
    "        self.model = model\n",
    "    \n",
    "    def forward(self, x):\n",
    "        return self.model.defunc(0, x)\n",
    "    \n",
    "    def loss(self, y_hat, y):\n",
    "        return ((y - y_hat[:,1])**2).mean()\n",
    "    \n",
    "    def training_step(self, batch, batch_idx):\n",
    "        x = torch.randn(32,2).to(device)\n",
    "        y = -(k*x[:,0] + b*x[:,1])/m\n",
    "        y_hat = self.model.defunc(0, x)\n",
    "        loss = self.loss(y_hat, y)\n",
    "        return {'loss': loss}   \n",
    "    \n",
    "    def configure_optimizers(self):\n",
    "        return torch.optim.Adam(self.model.parameters(), lr=0.01)\n",
    "\n",
    "    def train_dataloader(self):\n",
    "        return trainloader"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "hdim = 128\n",
    "net = LNN(nn.Sequential(\n",
    "            nn.Linear(2,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,1))\n",
    "         ).to(device)\n",
    "\n",
    "f = nn.Sequential(\n",
    "            nn.Linear(2,hdim),\n",
    "            nn.Softplus(),\n",
    "            nn.Linear(hdim,1)).to(device)\n",
    "\n",
    "model = NeuralDE(func=fLNN(L, f)).to(device)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "GPU available: True, used: False\n",
      "INFO:lightning:GPU available: True, used: False\n",
      "TPU available: False, using: 0 TPU cores\n",
      "INFO:lightning:TPU available: False, using: 0 TPU cores\n",
      "\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 4 K   \n",
      "INFO:lightning:\n",
      "  | Name  | Type     | Params\n",
      "-----------------------------------\n",
      "0 | model | NeuralDE | 4 K   \n"
     ]
    },
    {
     "data": {
      "application/vnd.jupyter.widget-view+json": {
       "model_id": "e7eb66fa2424408f85cf82006a4d6c4d",
       "version_major": 2,
       "version_minor": 0
      },
      "text/plain": [
       "HBox(children=(FloatProgress(value=1.0, bar_style='info', description='Training', layout=Layout(flex='2'), max…"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "C:\\Users\\Stefano\\anaconda3\\lib\\site-packages\\pytorch_lightning\\utilities\\distributed.py:24: UserWarning: Detected KeyboardInterrupt, attempting graceful shutdown...\n",
      "  warnings.warn(*args, **kwargs)\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "1"
      ]
     },
     "execution_count": 29,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "learn = Learner(model)\n",
    "trainer = pl.Trainer(min_epochs=10, max_epochs=20)\n",
    "trainer.fit(learn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "NFE: 76\n",
      "inference time: 52.34833216667175\n",
      "avg time per function evaluation: 0.6887938442983126\n"
     ]
    }
   ],
   "source": [
    "# Evaluate the training results\n",
    "import time\n",
    "t = time.time()\n",
    "model.nfe = 0\n",
    "X0 = torch.Tensor(64, 2).uniform_(-1,1).to(device)\n",
    "s_span = torch.linspace(0, 1, 20)\n",
    "traj = model.trajectory(X0, s_span).cpu().detach()\n",
    "T = time.time() - t\n",
    "print(f\"NFE: {model.nfe}\\ninference time: {T}\\navg time per function evaluation: {T/model.nfe}\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, \"LNN's learned trajectories\")"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uq0b2O8GqVZvfvbysJvhJq5dm6I+ZYcfV8TcRvaaOGqeFN5tkB7WaroGzWRXQqJi1MWpWb2+r0M7Oqvbe27Nm+Nzc8Pmrxg1aM2RyiQNm/A3TEy4iD8bJlQjCJJjZCUYEkh0sLlpTcmUlmryAZqfrBNvZsU6zTEa1/Ukrq8xmVUPX6/GXE6urlnF1EpAI8wSDhASDhogYw+SaemeneykgnWCZjGrkrS3VQHS2bW6ePMcYowP1erz9CwWbuTcJGPuaOUE4aB4DnZlifPW6thOxhRdxVlcU3q0tW9g/O6tae3PTarFq9fiuM11kMpbUoVTqbj4XizYJZxKKNhJhPmL4a6MBKwisg2axx+JiZ1FGq2VT/kQ6ebczPdzJXtZ4NLvpBFtZ0Qe3WtVxkhRhdvZkCHSlotZQva6/MQq0eGo1vU+93INRIBHmEWB//3B9dLvdW2jHrYXOZFSYmHbo5m5vbemLRRluimerpecdhoe2WLQmNwW6UrHsHWtr+tlxEWhjdKzttv7lBMdU2UYjXvcQhu7qdcuLPi4kwjwEMH+aL7c+msLIMjeRzvpnV0MHfU7Bdc1i1j/zYdvb03UwHyqai6zC2trSh45kBf0im9V19OqqvmZmbK30+rp+Njc3+Swmu7s63vl5nZgKhU5BrFRsaK+bdiZVcqNhJ7c4MMaWYA5rAkyEuU+4HNdMzEilrJBRO1I7U+D6SbwgKQIFnE4XPgTnzqmgHhzYMdE5JaKfB9EK9QOuo9fWVCD29/V4rkDPz0+2QE9N6XXk9SCNEM1kNiGIq53dTiNh7J/G6HMyNaXHa7X0eg2z/WwizD2ChALNpt6gTEZvZqGgDzDzfLe2OlkzXe2cTneyl/j5xfzMJWQsoclOIT44sP2rsllbp1wq2YwmtwiDQk0HT79CnUqpwG5s6O88ONCHeHbWJp3Mz0+uyZ1KWSEmUQP7OhO9aOd0Wu8ttXPQ7z440OtSqdgEnnRan6NEmI8YJM7b2bEFD1xHstCdIQqaufQ6p9N6M7mGpSnOVzdQ6DMZPZ5rmu/t2TBTJqMPCWuep6etQ2d7W/clpVGtZjVPqdSfZ3x2VsdFr/bMjH62tmY19KQKNLWpq50rlWDtHId7vFSyTQGDWFtISsHjAbYEc39/OIkniTB3AYnymk3LS02Tdnvbar5MppOah2ZVrRa+jmZbV5dfjPBr5oMDa667pjr5yrg/a55ZOslJp1i042m17OSyuanf4dh7BcNSjM3OzOi6meWVk+oUY6FKrWYJGvzamWmx5FKLQi6n93R7O5yCqVhUy2V3t5PLu9kcDltoIswh4JqKDylzng8OVABYMlgoqHBToCgwOzvWY5rL6T7kGxv04XbZRBmy4mRBDeK2gKX5XSioWekK9f6+jrXdVmGuVnvXEiQyIP/z7KwKNSmJXAGZJLhr3SDtzKUR2U673bdSyVpoQSmzJIhsNKzwZ7PWQhoUE+GmEJHXisiXReQxEXlHwPa7RGRTRD7rvd4Z97v9YG9PvZy1mt6AxUW9yaTd2dmxZPQzM53OrrU1FZZiUQXn3DnVTuVyf4keQUil9GEol221FMfi5xfjuDY3lSx/Y8OmZjLHmg6Zel1/X9wMKBeVigp1s6nah/zcXIJMIhgn3tmxXGD+384JPE5FFT37YamunPxdR2ixqBPpMLLIxq6Z43CAefhjY8xf6/O7sdFo6MOXSunD7jc9i8VwD2c2qybbOIoQuMZjdlerpYLEB4dONhL3AYf5wRgGo1ecRRZxUS7rOWo1fXBnZmx6JIkAJg3UyI1GcIiJ1hS1dxSYC99o6O8OWmczw4y9wAoFu9QZtEvlJGjmr3KAGWNaAMgBNurvdoDdFjc2bDzVL8gsCYwyQyehmoimPftTMfyRTuvvXF/v1ASlklofrKiix355ufeCCrcEc2tLj1ko6PtJZC2hZ7vZ1PtNTnUX5bJqzzi81m5r3iCQ342aXkTPy2XZQL9lsK8PBXE5wF4pIp8TkY+IyEt7/G4kBxibXXNWHlWcNO7NGmZVKk07toktl1X7rqyox9mNkVeran67XnrGjnuJj09PH86MymZ1opyUogQXXA8zTLS93fl7ORHGmdj8whqEYtHmH/D4dEgOgkkQ5jgcYJ8BcJMx5nYA/xbA7/fwXf0whAPs4MAycszODp92lR7m5eVgKlU6zba2VGiuXh2ccjUM6bQKGvnD2m2bzcUHiVYJmTuZD7683NvDVq12amRmhjHRZJLALC4KM++ZC0YD4lSwUVjDOk7S4qP25np9UMtlEoS5KweYMWbLGFP33t8HYEpEzsT5bhQODvRBbrdVcw0reK/j1JmcTidjrKOMZtjamgrv6qqN1fZDeN8ryP/FOue9vU7ty+qqhQWrtcjY2YtzjA65rS09xvy8TZ6YNE6MUsmmz2azh7Uww01xHGHMhQ8TTsacud11jA2CsTvA4HCAAXgWygH2ve4OInIOwDVjjBGRb4BOQqsANrp9Nww0rdvt4TNnsOsi2T2Y8bO/b8NaZKgoFnXbODor0JvLrDL/0mJqSgWaLW5ofu7tqaB2G6+IJTkQsf2w1tb0mOMuTHDhhqGmp3UCdtvX+JM+on47ow1R+7ImfG/PVr8NykE2dmGOyQH2NwH8XRFpA2gCeKNRvqPA78Y5L82g2dnugsxukN08u6S93dnRfenZ3t/XzxsN6/CgEPcKtzkdwWZ2/azzaSXs76sZPT3dyfFFrzQTXEiWsL8fr6iCQkzk86rt63Wd6I6yxxUz38Ja2jJMZYxdI1OYl5ZsVGBnp7sVVyza1N6gZBx6sZtNvd68voPgVHOAhYUPXHBNDahZGgZW4hijs3GhYLs/0jSNCmsFgQkhdJbEKaP0l03yxQcxiIyPSwKa+mE9nPf29DdSQ5fLOmH1U8fLdTrZTI4C7Tbw5JN6b86fD95naclOuLWa3vNMxoaPABuCjIIxusTK58MtEC7xzp7V/zXBpn8OsLFr5nEijiCvrqpQRt28et3WFM/O6o18/nlrSlI4ugkxnWGsxKLgsv2rv4ySGtqNIxNuAzoWY+zt2bG4dc9cQ5M5Y3s7uIczk03SafubjVEN3es6f3ZWBWd9XY95FEsM9sVeWrJC6gezuOgIZaor48OplE3Pjbqf/pBT0O8rFFSASWww6FLvVAtzFPxr6rCHleYza2K3t9Wp1WjoAzs/3z3neX/f5nnTWmCxRCZjTWDWJ7va2c9aks9b4SBJQqtlCyI2N21HyHJZx8yKL4anSqXw7pBMpkmnVfBZNdVrskwqpcclv1i3yqRhYXFRz7m8DFx33eHtxWJnu1eue10LB+gsmAgDvx9mavN6MaMwEeYRgTHRKOfY+rpNkqfT5Pnn9YafP999TcmSRBZrsInb1JTVrIwDu1oYsALM9TL/bzZ1DGTPyGRsEQj7NjPLzS1XZEkkv3PmjN3P38OZ62haCQylBWXMRYG/l2vTo0i44VJndVVTbf0ak55lTmLuupehNvoO4hRfsCw26LqwSIbCPOiaORHmADDdrlIJfziptZjxtLamQpTJANdfH16kTjBDimtUPhjb2zZ0wweN71kGyQL3TMZWW7n7sv6ZNdBuyINe2euusznHTPZnxQ/TGemko5be2dEHnA+dm/ZIMoReNTQ7aWxsqNY8CnN7cRH4ylfCi0D8KZmNhnVa8ncynzpqeRHH1ObaPI7/phsSYfZhb09vWD4fPvNSm7LQnIKczapGjsrhpWebZXBMD2W2FD2prhZ2a5SDHFgUXmpvepBdgkBmGHFN7nrWCwX9HcxRZt6w28O5XrfJI25XCxYXAP0JNLX8ysrRhauqVb1Xy8vBwkyiB9Ym0zHIkBNZXkgKEQWa2q1W8DWhMO/sDO7ZT4TZAfOW+YAFgR0iqME2N3WNHEeQAVt6yLXp7q51srnVV6y3DaJ8pVDS0x0n1ZJsnjS5RewavNVSj2q1amt8Kdh0/rDqa31dBc81u5kuCnQmiMR1irHTxlH1SOb4rl4NN4GphVkc4hZG7O5aU7ubBcb8AU7eftDKYqXdIEiE2cH2tnV4BZk87bYtxKhWbYZXOq1ma5z+umx/kslYPmomLHB9TNPdNctcGiAKLz3cXBe7JrdLbkBzmyY3vdyZjKXRJdJpncjo1aWDj/HhhQUVaHph+TBToFn2uLZmO2DEwVFXVFGYV1aAG244vJ3rY3qad3b0mriCTwdjVO8t8p0zOhCEXG7w7C8gEeavggkFLAsMArX27Kze5KUlvZnnz8d/GClwLHLI520iQhA5QLttvaushioUBksyIHXR7q5de/vBMBTzyp9+WgXg+uv1L0nw9/dtNpjLbMJCDjZ2nzTQGlhf19/kX8+m09aXUCjYhgT0OTBPnUkfUWC2Vxi3Ns8TlssdFxN4mccDrvfCQiTs6EDyd+ZTnznT2zrPLezg95geyZAPoFqVnuRWS7X12bO6D0NJ/YLMI3Hiw8Wiaq4zZ/Q3P/KIPsDVaqcWdmPcmYwee1LzsAl698Pa7BQKnQJI7cliDHqqu4HmdVh7XW4/CVVTY0e7bddEQes2V2tzll5dteWSfu6uMPhj18WiCsXCQud6aW9PhZgF8WQ6GZeGS6eBCxeAW27RsT/yiP5+xqm57nfX7tmsbiPP2CSiWrWN5oPAlE0KNAsjXMuNqa1R4DIoTJhpHXXrpd0NiTDDMmOEmcqMo7LCaGVFBcu/JjRGTdKwyiKSArhrL9fMZVol00fPnLGWwCSgWgVuvVXH/tRTwHPP6QM/O6u/y6+FCwVLVDCORua7u7ouDitbZJLM5mawE5E86FwCkQiRGXlEHO2czUZr3m7b42AiHpMYHGDfJyKf915/KiK3O9ueEJEveNxgPTdd3t+3WjnM6dVoWK29tWWzu/wOr3pd9w9aQzH8wEws//rIGBWQxx+3NcWjLoXsB9kscPGiWhZXr2qucy6n/7daqqFdgZ6e1u2sEDpKZDKWAikMrOoKsx7y+U4nF7UnfR30VHdDLmcrzqK2D4KxC7PD4/U6AC8B8CYReYlvt8cBfJMx5jYAPwvgHt/2Vxtj7ugnQZ11q0GeaJfPqly2XQhIyeP3Ntdq1jnlggX+jPcWi4cF/plnVBDYZZFx40lEKgXceKM6/tbXgStXbGN2XiMXbCrHQpSjglu2GAY35BYEWlDUyNTC/JzC3O13cWIOE/xuTrQ4GLswIwaPlzHmT40xvNwPQEkIBgYZJVjA4MfaGvDss1ZrkzVjZuawx5vxVb8DjbHrVMoSFExPd958Nl5bWFAB2d9Xwe7WQ3mcENF0yBtuUEvjyhUbsmM9N5FK2QjAUfd0LhZt9VoQSMTALCw/3PVuLmePMzVlLTmSGkSBy6kwU5qhxUEwCcIcm8fLww8B+IjzvwHwMRF5UETe0suJWZkUppVXV/UmsN3L5mZwZhiTL4Lyaxm+IViMwfpYZmNduKCCwUotoHtCwiRgYQG46Sb9TVeu2Hg0yQwIcodvbw/u6OkFbMwWta6dmdF7FObroBBns52msrsMivObuq2LB9XOkyDMsXm8ROTVUGF+u/Pxq4wxd0LN9LeKyDeGfPcQoR+7VARl5lDIZmdtumVYvna9bjO2XPABYXsatoFhYT7DT9msbda9vm6rkMbd7zcu5uasQD/+uF4Hxlbdh3d6Wn/TUTrDmLIatW52W9MGIZezoSigky+N5ncc5xWrrsK83yeBajcWj5eI3AbgfQBeb4xZ5efGmOe8v0sA7oWa7YfgJ/RjS80wxoi1NVumZ4yah0Hcz8yqCurXxFxr5kgz/ZPmOOuBGW+u1/WhcIn1R4mwWuh+MDen1kWtpo68mRkb9nG5xebnj77DBZ1VYQJHut0wIkUKWbttUy+BTiUQV5iBcJP8JGjmr3KAiUgWyuP1IXcHEbkRwO8B+H5jzCPO5yURqfA9gG8D8FCck9JpEZTttb+vgsaqITYEY3aTC2oZv6nOiqRMRh+CSsWSzJOHmeWT3IcOtGESC0aBoZurV7VQhOmNLk9ZL2AHj7U1TXOdndVjuM6lo8q/dhHH1K5UbL67HwxFsViC+7ithuKsm7l/mOAfe2E2xrQBkMfrYQAfJAcYecAAvBPAPIBf84WgzgL4tIh8DsD/AfCHxpg/inPe3dqcnDwAACAASURBVF2bN+sHiw/osW429UYFJW6QPN3/udtKlVSu9GhTC7imObtoHFWRPmCdcewWyYmt0VABvHZNBbOXvGG247l61ZLj7e72TqY/TLj50WGgfyLMQcf1Lk1rxq7d56ebMLOaLWy/QSe6iViVefS59/k+e6/z/ocB/HDA974C4Hb/53FAh0ZQjakrdGwgl8kc1pikjwkSQDZsa7dVYOlRdTW0W73E/48yQSSqZQydekzXZB/qbpU9Ihq2YuO6xUVLtxsWNTgKcAxhdD8sWGGKrh9++t29PVtbzpLIOHF0khGMAmPXzONCux1ec1ur6c2jSUXB95vkbvGDC2M6iftY7A5Yjy5pbnk+Th6TAhYiLC7aOPHGRjwy/FQKuPlmu2bmZDfOtE7eu6gQFe9NEPyMpRRcdv+MMp9dMJFlFDkEp1KYaf4GmdjUmsWiJW/b3Q3OEGPsMYh6hlqdNcQ0x7l2Y1E/K5j6aXh+FGA11MKCXQNzXR3mNKOHd2bGZtBVKvq7R6WVuoFx3CiBKxZtjXjU96mNgU4hj9PtghGKOPv2ilMtzEGhH95Mmp+8aX6tzBrhMO1O7ylzevf3bdcCY6zJzpDJUfJH94tCQTU1NdjKyuGHstnUtfbeno0tMxQ3jGKCQZDNRp+fXSzDQmdcNk1N2d9NRhdAv9tNSBNhHjIODsIzbkinQ2GjR9qvxd1YYxDcHF43lLGzY2tlAXUUkXzvOIBhtfl5naBWVjrjpqyzdjnEmT3HwpFxIZu13GhB6NZWZmrKrpVdU9lVCnGEmRbZsHEqhRkIT8hoNq1jo922Sfb+sAGdHmHhBHc719w026nNGw1dLx9FTHnYyOVUOP1lo655TSbL6WnrexgnOIGGOap438OEOZPpJObjcXoRZkCv1yia551KYY5qNbO7a3mZSLXDda+LbnQxFGC3GRn5uijMDIMch7TNIGQywaSHbupmq2VbxI6qu2VcdEvaACybZhD8z4BrarOCKo6QJsI8ZISREFDwaAqFrYvDKGAAu3aidqcjzPWAAvqw53L9pfG5HS8mESToowe7UonfsHxU4HImSnsyghHk3HPvtyu4fJbiCnMqlQjzUBEkiFxPUXhdQXTB9VKYMPNG+QV4ZcWa8YClcu0VLMYYZyJGN7AaaW/PZs/FbVg+StCJFQY2+gvS3hTa/f1OgXQVQ6KZx4Ag5xdriKkpg26W+3mYMLvml3sMxpN5jFYrPHWTHGNB6OZ8mxTQvObvKJXiUwOPCt2Emdc0LIRFze4KpFsKGVeYgeFfh0SYHVAzu+GDIE+z/yYGHQfovPFMAfQzVoSFtqLM6KASvElFuWz7XZVKSko4ThokOrHCri3vR9i6mgQTrjC7ZnacohX+/kSYh4QwYQaswLGiyS9wvAlh4SS3eTlL3p59VteLfibGsPU4EK75GR6ZxCQTPxjuYchv3GPuJkjd4sC8pySbcI9JdBNmNy49TJxaYQ56qLgWci82OwC6cFutBsHtG8QJgsLLhyUog8h//KDJYnNTTfAgQWd99KDEcMOE229pEuCue4PAdj7dNDO1MBGXoZXHAE6oZo5B6Cci8ive9s+LyJ1xv9sLeJP8Ddv84M0K0zI8jvueAk4hjBLYKDN+b8+2rwk6L7tyTBJIVjcJ4+omSJzMo4TdJSpwtTPfdxPSE6uZYxL6vQ7ARe/1FgD/vofvxoYrzFECGybk7nZX2FzHCIW33bZaIOj7QLjA9rNtnIgT3z0qdBMk//0P2u7v0Ol+L+rYccfQL7redhF5nYj8maf9PigirxzuELoT+nn//6ZRPABgRkSui/nd2HBvzCDCHLZvL9+JOnfYNpfRY5JAa2QU4ZheEUeQaEofN8SZw38NwI8DeAWU4vYXRORNQxxDHEK/sH1ikwG6HGBra6tBu4wUfkHrd1aOM5FMmjCfJPi19iS13okjzNeMMX9ijFk3xnwCwLcD+OkhjiEOoV/YPrHJAF0OsLm5+cgBBZlRHYOJMMPC4F9jRQlc1LlJlhCk5bpNFEw2OWpnFK/nJEwyca5/1ITZi1V21IgjzE+IyD/3+LkAYA/AMLNs4xD6he0TiwwwLoZ5k/wPDR0k7rqWbVfDxhG0jU6uII91nPXg7m7n2rXVGj2XdSoVv+XtqDEsYfb7Ndxr3u05ijOGfhBHmA2A7wTwtIh8GsBjAO4XkYtDGkNXQj/v/zd7Xu1XANg0xjwf87uxwbXSoJrZ9Wz618uDCnNUHNQfDvNjZ8c2riP29lTTH8c1Yj/o5ldgqm5YDoFfmIPu1biEuSsHmDHmTXpiyQN4GZRz63YA7xORW4wxF6K+H+P4bREhoV8awPtJ6Odtfy+UH+xu6ETSAPCDUd/tdyzpdKeA+WOJhBveCPIcuw4UN2PIDc+4QunP5IoKn0R5htPpeMn+rpntxr3D+lKfJHRL+OmWd8+Ih197u+HIbtGEsQmzHYDZAXDZew0VMQj9DIC3xv1uvHMevpgUZr8g+tFNmIPMMKYR+oWZjI/+cQDBQklShSiGx7B4Lks5XSYNNxf5NAhzWL494a9s88NN5fRPukFCHnYM7j9MTFhE8ugQJKTUbBQG11x24TeZg47DSYE3nH/9edVBgufGov1gAX03apuwbSzx4zhIQztu4oCjAvPtw7Rnt5x5t2IqqGDCzSAMQzfroF8kwuyAN8IV5jChDzuGu9294fzrr3gK8yyHlclRIHd3g4WWNdRhY2Phgyu8bFs6CXHgUSMOqQQQLMxM/iEZQZAFFUdA3dz9YSIRZgfptC3b4/9BD3i3/F53u0s14xLasbtgVHeDMM1MXrEgbdqNGof1025dsct3dpJB1pcoYW42LdOMH/5quCBnZFxhHkWW3qkV5jAhZb9e/r+/f9jU7pa/65rJbnkc+ZZdqt8w85bmctC52ZUyqNC/Wx/gfN4SwrvmXrc+xicBvPZRpaONhq30Cvq+C1eY2Z0kTmuhMCL+QZEIswN/aCdKA0c5mphz7c7eBwdW2/J7hUI0E2QYdWulEk4J220NnE5bDmv33OxjPCnVTaNAt/UwOczD2F/29jqdm25kgR0/4ghzFOXUIEiE2QGJCOIIczfGCm5Pp60mz+VswzhAb3y7HWxqRzFe5HKqYTc2gh10uVw0o0dQhwm2jgljNzkJaDYtFXAQajW9nmEEiyTApyamQHYz3V0w9DUKRtZTKcxRvMWukEYlaISZwVHHyedthwfAaoAgDctJIGjtm8vZhuZBmpQhpjAty26WW1udXu1yeTIocUeBVkuvfZTm3Ny0fhM/XJZVMrgC8Ux3F0H0vMPCqRXmsPWuK4T+UJUL3syw47iNtWkykx3E1cwi4SR3YeZyJqPaY28vOBXTbYkTBHJb7+x00t8Wi5arLAyTRHzQC9jfK0yYDw5UmKvVYM3NFsB8PvyMMXGFOYqUYlCcamEO0qrM1KKJ6jJsunBNrCC4ZjJvHPv8bm/rudNp1aJhpi2ZIoMmE3aQ3NgI/m6hYLtUBmF6Ws+9umr3IaNmqxU8EdTryjB63DQ3lzZR/bw2N/U6hDWCZ5NAPheu9ZPJxHdotVrh3VQGxakUZiJK47omcpiZTe90ENzt7qzNpmOcoctlfdDC1r5AsPAUCvrdjY3gMfh7WfkxNaV9lNlVgygWddvW1uExlUq2s+MksIbExdaWXUaEYXnZdr70wxgVWoYEGVY0pvfMOTZsD8Kg+fGnUpj97UVcUJhdc4jmsv8YbjfAoHMwjuzOxMWinpemdaWixw/Szpzxg4Q5l1OTcGcnWDuzP1ZUuKla1X1c7czP9/cPm9siOgEAWrBxHIoz2HmSPa+CsL1t+zIHae6dHduJZHfXTpRsAhhXmEmuH2aSD8rEMlZhFpE5Efm4iDzq/T1k5IjIBRH5XyLysIh8UUT+gbPtXSLyrIh81nvdHe+84WvhVEoFyJ+jGyb4UTeAXmXeQN54Y6ygVCo6lrDexdQGfi3pF6wgFIs23BI2vrk5fZDdtXc2q9+t14Njq3NzKuyrq5Mt0Pv7OtFNTUWXXz73nO4T1GQdUGF3oxyu49JtAtgNYf28iUGXL+PWzO8A8EljzEUAn/T+96MN4CeMMS+Gsp281cfz9a+NMXd4r9gFF5lMuCD6O1GIhIeP6OUMAre7plU6bYnhuW4uFsOdThT+oBtdKulksLER7LkuFHRyiuoiMTur51he7vwdbC/Dbo7+3zU7qxPFpGpoY3Rsxthm8UHY3NRrv7gY7GEm53exaNsJUbCjYtJB2NmxDQTDtg+CcQvz6wF8wHv/AQDf4d/BGPO8MeYz3vsagIcRQg3UC6K0qtsjiuZyHJPcD9cJ5s7G/nTMalXXtkHn4M0PWvtSszabKnR+iKjA7+yEr3GzWdVIzWanhvd3c/Qjn1ch2dubTA29t6djn52NbiP09NP6WxYWgvdhTJjOL667uSyKK8wcT5hJHubo7AXjFuazHskAvL+LUTuLyM0A/iKAP3M+fptHv/v+IDM9DGFrYeBwwkY2GyywUWtaQAWC4SXuK2LXzTStmcQRJpBuk3Y/5ub02MvLwQJFD25UMsjMjD6kq6uda2w3nh00mVCg2+3gxuvjAqmVSqXo9SyTPW68MVxb5nIq6Awxkja40bChvDjw9/32I8xR2QtGLswi8gkReSjg1ROLpoiUAfwugH9ojKGu+PcAXgDgDgDPA/hXEd//KqHf8vJyZIaVX+PSXA56WFlSGAZupwPFbelKYS4U9LOwdXOhYD2qfpRKKtCbm8EaNJXSh67RiM4lX1zUsfknhUpFf//GRvDvz+e18frBwWSErdpt/Q1sah+FfB544QujvdxEtWrX1FwixfkeoPs2m3q+sEmj0Ri83dDIhdkY863GmJcFvP4AwDWPMhfe36WgY4jIFFSQ/6sx5vecY18zxuwbYw4A/DqUejdsHF8l9FtYWIhcCzMezG35vHJYBZlrFNAwk52aYXfXvk+lbGEDv1et6kMSJDDZrD6YYZliCws6hqXAq6cPnUh0Mki5bCcF10IQsWvOsPUxTfVUKrrh3ShBbczJaH4+HudYLwUPdJpub3dW13VDo6Fjisr57padFgfjNrM/BOBvee//FoA/8O8gIgLgNwA8bIz5Jd+265x/3wDgoV5OHmY+u9u6MUt2q1KamtKHnH2meKxyWb9DbTw3p+cKSwIpFsOTQKandTIIa/NKJ1ujEW4Ki6hAFgrAU091avl02nqw6VTyI5PRSSWf1++GCf7BAXD1qv7OYWSTGaO/eWlJz5vLqZUR5jEeFLxfYfnbQajX9TkJG1M3Ezwuxi3M7wbwGhF5FMBrvP8hIudFhJ7pVwH4fgDfHBCCeo+IfEFEPg/g1QB+rJeTZ7OdJYkucrloTzWRTqvARnki3V5LPG6xqH8pNMWirl3DTOGgOmR3rIuLKuzLy8HfZwgsiokzm1WB3NwEHn20U/CzWR1fqxU+4TBcVq3qWJaWDl8XY3S8zaaa5VevqiUQNdH4sb9vnX5Xr9qc6vl5Pf+oOnpsb+vvmp6Of45mU8cbZpJz/c3IwyAYQbp3fBhjVgF8S8Dnz0EJ/GCM+TSC+bFhjPn+Qc4f5m12t+3udl/L5PNqwoZxghUKesOYcMAHvFq1Qi2iglSrBde7MvWz0bCC6WJmRs3KpSXg3LnDjh/W29ZqwbxjRLUKfM3XAI88Ajz+uK4pea5CQce2taXHo+POj1JJr+f6umrofF73Taf1NTtrfQA7O3pd6ABi5RoLTQiyfLCHNn8Ti0ZG3d6WefC5XHzKYE7WU1Phjjim9sZdf0dh3Jp5rMhmLZe0H64nuhui0i55HoaX8nlraudy9mEGuqdglkr6IIfFlM+eVWG/ejX4++WyCkmYow3QcV1/vR7r6acPr8PLZevhjtLymYya7dPTVkuzxJDnKRRUsM+dU8tidtamjNIqIl8Z2TkKBZ0YFhb0ezMzoxfkgwOdmBiuiws2Kwib9MiBns8Pp4pqrJp53GAh/85O8Bool4vWuASFdWcneN0jojeMQkqzO5fTG95o2BvKFMygmTqXswkn/vOIqJl59Wq4dhbR37m+rg9RmIbJZFQjb2+ruV0odF6f6WnrcOL/QaBvoFBQwa/V9Jjl8uGiB+Y7D7puHAVaLRXK+fneHGbM5w6bbMhXXqnY/QfBqdbMgCUMCFqrup7obqCAhtU3M7zErCFmfwE29xewlEBh5yyVrMbyo1hUIY7SzgyDcZIi/LXRxSLwtV+rY/nylw+Pp1rVsdTr0RlmgDWtFxZsEce1a/r3OJAI5vNqqfRqAZw5E67J9/f1uhUKNhQaFW2Ig0SYI0xk1xPdDVGxYJ6H4SW+Z652s2nDToxFhhVIFIu6PSj8Q+1cLquwhB2jWtVz09wmBdHGRqdwzc2pht7aAh566LD5X62qVo6bBTU1peM7c0YFo17Xca6thVeOTQr6cU5FMXD6veJumLJfnHphpsBGEeAFFTr4QTqaqEweOr8ODqzwZ7Od7CPMEKMX1A83RTPo5heLGhNvNoHnnw8eB/mqmk2b/E+nlOupFtFj3XijOsM+85nDHmfGsHtBNqsTxdmzlvqXnun19clLDe2GXq0LXvdKxdbPb20dg6SR44Aogc3n9WLHiYmSECBM8N1qG1ebkRWEEwrXsmHma1SKJsNDMzPWlA1Cuazn3dy07VgYUnLNvXQauOkm4AUv0Oqi//f/hmcap9Oqmc6eVY3NNNdJaxYfhc1NDQcGXZMgHrb9ff3O1JT1i5ApNcxRFhfH6LKNDlECy0SPOLmz3Uxt18FFMnt+b3fXaud02oazgiYG0u02m8Gx2UJBNereHvDss8GajtqYDxegwlQoqDC7lko2C7z4xcCFC8CTTwJf/OLwTWLWZy9GZudPFjY37brX7xhrtzWJx59vzyo0Mprs7FiH56BUQokwwwpskBDSEx1n3RyVdkmUy9YBxr/URG7+NMNQYceieRumeWdndW26sqKvIExNqanXbNrJambGsom42iafB/7CX1At+uijKtSTvMYdJYyxEYFy+bBGZa030Llta0sVBq8x660zGevRHgSJMKMz5huEQkEFK45XOyrtElChoCC6Mzo1MU3rbNY6icK0c7kcvnbOZlU7p1LAM8+ELxNI+k8OLJrpfGDdc5dKwO23Ww397LOnT6BZIdZs6hLBH5ZzSRvm5zvjx+22XkNacLy+c3PDaSKXCLOHfF5vRBi1bVxTO4o+NwjUwOxf5ApvuWxTF4NQLquwhmnnalVDVVtbKnhBcJ1ffLgyGf2s1TqcYDI9Ddx6q/7OK1dOl0A3GnZ9PDd3OBeAgs6YtN9snpuzwu/X0sNAIsweGFMOEhzX1O724Pba6qVYtBlhDFNRO+fz+kCEVSG5BRtBVkM6rcJcqdgc5rAxM++azq98Xr/XaBw+f7UKXLyoE9GVK5opdtw80L2A619SELGgxMXurgqyMTb0FgRq4Gw2fgeMuEiE2QNT9cJipsVieCpl0L6klYlzXt5QkuQzXxfQG+52wfCD6Y9hgloqaXpmqxW+dgZ0DJVK50NaqdjsLf/5Z2Y0Bj0/r8d98smTJ9Bc0y4tqcXGmma/s6tWU2FnOWocR5Y/q24YGGs6p4jMAfhvAG4G8ASA7zbGHOLbEJEnANQA7ANoG2Mu9fL9uIhKfnCTPrrNpkz8IGdUN1QqemPp2eSL66taTV9hqaLT05p44Q95EfPzVqDD9uE4/GAl18bGYfK6mRk999KSxrT394Gbbx5ut4ZWq7MVzFGg1bLsKozrB7F7ttu2lLNQ0Osx7AbqvWDcmjkOoR/xao+071Kf3x8YDCF100BxuLdcsEKIFUCtVufaeXq6M7HED+b/up0dXUxNachnf18Fr5c4MR1i6bROGH6fQiqlpvyFCzrmxx4bLtvI5qaOeWlJ37upr8MCSReZZkrGlHJZr5u/ywWroZaXLc9YFGngUWHcwtyV0G/E3+8JvTi3enWEAXYNPDWl33MLM6amOquO/KhW9SEPy++tVFRDkzigF6RS+l0RNSeDJqgzZ7R0stXS0NWgecYE66MzGb0ma2u2mGR9XScQevTjCDlZYZpNax5fvaoCXK/reWZmNARHhlKCxSXXrtlil8XFySkOGXfVVAehn4iEpQwYAB8TEQPgPxhj7unx+xCRtwB4CwDceOONfQ22W1WTCzfxI6j+OAzFomr19XVrWtOUJuFeULUTuaFJaeNft5FJhB5ZnicuWPy/sqLj4NrRrb2uVjVT7M//HHjwQU00WVwcTGOl0zrOUqmzLJIv/1qezkS/SWyMCrJ/Mpya0muRy4XT4NKP0WxaDjdyo00SRi7MIvIJAOcCNv10D4d5lTHmOU9YPy4iXzLGfKqXcXgTwD0AcOnSpb6DKcWirpN2d7uvh5mlFSaAQaB29q+dczlb7RTGSsEEkM3NYEJ3mttPPaXa5cKF3rKOMhkV6NVVfZEnzY2nlkoaunroIeDznwduuUXX0cNoLu5vusc1Kntek7jAFVqX9ol9s8ldzhZCQWi3bQ9r9mXO5/X3TZoQEyMXZmPMt4ZtE5FrInKdp1VDCf085hEYY5ZE5F4ocd+n4BECdvv+MEHvLqufopDN9kcHUyzqi9qZ4avpadWq9XqwJ5TsH1H1ypWKely5Njx3rjfNyR5VNLeN0eO4cdXpaeDrvk419JUr+hte9KLeejKFgREFhu/olGPnS5fSOC7IWb23py/XLzI1ZSvDJj1nfNxmNgn93o1wQr8SgJQxpua9/zYAPxP3+8MGq5ooUN00TlhXwW7noJZlVhjX0uysEMYOSdN+a8s2UPeDDeNWVy33dS/IZq2Gpvm6sqLH5QSXy2m22OOPA088AVy+rALNtTdBZxJZULqBY3VN7SBzm1qYL0DPa4x9UZO7pjfzBPgahkVxVBAzxvQdEZkH8EEANwJ4CsB3GWPWROQ8gPcZY+4WkVsA3Ot9JQPgt4wxPxf1/W7nvXTpkrl8+XLf42631QFTqQwnpzYMdPKwACGVsh5pdrMIQpx9mk1N9jBGze1e2qwQ/m4WImr6+h1Cy8vAl76kGu/GG9VRRi2+u2sdcqQk6meNfXDQaW77TW6XrgjoNLlpdrMcdpwQkQd9EZv43x2nMI8LgwozYM3MQR08UdjZsQkLZ87YpH3Gnefnw0397W1dO8/OhntbNzY0b7tc1jh0P1U7rkBT801PH3YQ7uwoY8m1ayrwX/u1lgiROebNps05j+qlfJIxiDBP+CpgclEq6ew/KG9TFPJ5m03mEuS7tchhczEdNSygCAKJ8Q4O+m8Ax+6JZE5hrvjGRufY8nngttvUw91sKtHBlSuqmVkmODfXSStEjqwE8ZAIc58gAd+ouzeQjrfRsCmbIvo5QyZhmJmJJtYXUcvihhtsllc/IBMn+3cxU87fUE5ETfpLl9RiePZZ9awzM2193a7HjyNX2LiRCPMAIOXNKPsrkZFCxHJvA2pe00wNe9AzGUt1Gyb0ZChl4/Yo+twopNMq0LmcjT3v7R1uFQuo1XDHHcBLXqIT0mOP2WqjWk2FOpfT4+XznVxho7SEjjsSYR4AcfofDwOViuUFc01rrqGjeLAZo+6m3ZiYUa/335GQqZ9cGqRSNnTlz4QTUYvg678eOH9etfiVKzYllZlqjI1XKqrB19astp6UrpOTgnGHpo41mINdq+mDNapigHRaH2ZqWFY4pdO2U0QUWN7YbT/mgAcVVcQFPdpTU7ZtTCplCxKq1U7HVqGgQr24qCGsp5+2HSrYLjaT0eu8sKBanmWZTL8sFGzK62lGIswDgtqsXu+t20GvIJvmxobNAstk4oWUmFraDSQqWF5WDXjmTP8TFEszSXjAfPNWS89BwXPX/Rcv6nsK9bVrmiNNoWY+dKWi15p0R/Tu+2PE4woztVrWO+9nGxklEmEeEG7/Y2rLUYBOL2rnra3wGPIgYFHFyooV6H6Fgo3KWW2Vzar5vbKi14pe+cVF/T3b2/r/bbdpqOzJJ61QnztnhbrRsAk0vAbsW+VykDOXfmrKvoYd7grKF2eYjk0CjwqJMA8BzKWu1wenS41CLmeZRWhuj6JiJ5OxKZtra4eztnoBHWObm1YIGb7a3VUNy44XxaJtGl8qaUooiQ+eflprphcXdWz5fGczN/atYs9tvlgj7o6HKZ+ZzOFMMbd9LwXRTT5hQgoTVNx1eyaj48rnLdXUUSIR5iHA7X8cNy2xX5DEoFbTB39U5iTXrGtrKjCDTFJcRzPuzaIFNpSbnraOusVFnaj4+6an1Um2vGy19NWrKtBnznQywFAbMj7PxBVyu7GpOfOw+41hs1Ml1+vU+uNO/UyEeUhgZ8RRa2cSx5MNY2trdGt15m0Pq3E5HVvr67ap2sGBCm2zacntSiWb/07veqWimnpzU4WaFMLsr8Xv7O7a8NXUVOca2l/owbxyN0c7LPWTVVf+VrNx4D9et/36RSLMQ8JRameWVrI4n83gRoFhm/FMMKnVdOy8bjs7qn3d/OxKpbM5XbOp47ntNr3O167ZTDG2dyFvGScKTrA8t7uGprk97HtFS4CmPvnDgpyVBwfWkTdottvEc4CJyK3ePsQtAN5pjPk3IvIuAH8HwLK37aeMMfd1O++osom4dt7eHj5Zmx8MN9Xr6uEeZY74sMFyznxeJyS2tAVUyMlJTS415npvb1uhzuW0bc7NN+tEwLX2xoaNTzN2zmw9Njrwr6HdYoug9bP/ulKj88V1NIXY1cQchxs247KAvbnp7e+n2KXjuo65auo9ANaMMe8WkXcAmDXGvD1i/zSAZwG83BjzpCfMdWPML/Zy3ttvv2Q++9nLI3n4Nzb0YVtcHP0airQ3JFwfpXk/KrAEcnvbhtDIncaWNW5oh10+trdtphmJD0kHtLVlTfR2WwWTzQfocAOskLLiapBJnhMCNb7rPWfro1ZLhZcZcem0Xd9T2AcptBi3mf16AHd57z8A4H4AzhdnBQAACURJREFUocIM4FsAXDHGPDnoiXth/+gFrEOu1UYbdwZstRFjz/SiHicw5FYo6O+o1+3vaDbVQeayY7KqinF3+g34+4tFve5cO3PNXa/rZ67JTaGm8JGiyf8KGrO7jmamm6uh6aR0HW3U1KQ0HnaSy7iFOTaHl4c3Avht32dvE5E3A7gM4CfCqHZdDrAbbrg5lIljUHANSEKBUSYM0EtMZ9j6uq17Pm7IZjUmTY0K2G4f29t28mUXD8CG5hh7Jgmiy3Q6M2Pz53d39VoZYxvap1JWU9JL7RfgKHPbdZj5v8NQlbtWH+VSaORmdhcOsA8YY2acfdeNMYG8FyKSBfAcgJcaY655n50FsAIl/PtZANcZY/52tzHdeecl8+EPX46sBx4EBwfqmIkiBxgm6nU1t/f3Le3rcUa7rdp2Z8dmudGEZgfMUimYtI/dNLkWpSlLOmIR65ziXzdWvL/fyRsGHBZknpcZZ35vN9fe/WCizexhcIB5eB2Az1CQvWN/9b2I/DqAD8cZE02jen00wkxTkGbWqHOGaW5vblozdVLoX/sBk1ZYxcXEkJkZa77W65bEwKUFouC6TiausRmH5ouWGU1kxqFdc5lOLhf8n1Vpk4Jxm9m9cHi9CT4TmxOB9+8bADwU98Tlsj4koxI2el+3ttQ5NWrMzupvqdVsdthxB9fOjYbtGc1ML1eoSRvsLmmYZsu2uTSzKeDch902s1k9X5gZ7Ao1TethmswHB4Mvj8YtzO8G8EER+SF4HF4A4HKAef8XAbwGwI/4vv8eEbkDamY/EbA9FG6BxCjMUsZJt7eHc6O6gRVU+/vHzwkWBVamFQqd8eZiUSdJl/SQVLj+3+9qbJI6cP3MlE+CzjAyfdJR5hIDDgKXq4xZaVQoQfTIveBUc4AxhLG4OBpH1bBn7zhgAX9UJ8LjDLa9ZXM9al/mq7M9Lj+PI4Buuidf/jAVnWNBudzcDnTydbsMoIxHu+JG7/bUlKVlnug18yTDTcEcRRhpHEkcMzOaSbW+rt7h4+jZjgKTSGhZ0YvN1FN6vxmuyuVsx4qw+8EYsZvuSUH0r6Hd5JCgDhmEn3g/k9ExuEUew1Ygp1qYj6p88SiRSulDvbJi2TlPIris4FJme1stkmxWBb1atSb4zo4NV8WNxTO0FFfg/Bp3HDjVwgx0pglOkmdyEGSz+luYrzyKePqkIJWytdFcO6+v24KUc+dsuIrbmRE2zFLFSUilPfXCzBRCJnmcFLOUdc8U6JNOqUNHGVvpUmgBG4qiV5uFDY2GJTSkYB9lH+hh4xgPfXhgCmZYD6fjCtYjnzZQ6/rherXZk5nhKpIiMlyVy42OnWRUSIQZtsj8pGnnVGrwcMdJhZtAMj2tTi2Gq9yaaK6ds9nOsNUkPiOJMHtwCySOY/VRgsHAnHqWIe7v25RPMoK6Ti5ypU3S8iURZg+MTR4FuUCCyQd9KW4mndv6td2evGckEWYHlcrREPMlOJ5gPHpSM+wm0PIfH1jo3mgkvY0SHD8kwuwDGR1rtfGOI0GCXjFWYRaR7xKRL4rIgYiE5qOKyGtF5Msi8phHL8TP50Tk4yLyqPd34Hwnl5gv6WWU4Dhh3Jr5IQDfCeBTYTt4vF+/Cq1nfgmAN4nIS7zN7wDwSWPMRQCf9P4fGH6uqAQJjgPGKszGmIeNMV/usts3AHjMGPMVY0wLwO9AucPg/f2A9/4DAL5jGOOidj4uyQIJEgDj18xxcD2Ap53/n/E+A3wcYgC6cYglSHBiMfLQVBQHmDEmilnkq4cI+KznImyX0A/ArojEZiUZI85AOc4mHck4h4db+/3iWDnAYuIZABec/2+AEvsBQGwOMWPMPQDuAQARudxvAfhRIhnncHEcxikil/v97nEws/8vgIsi8jUeQ+cbodxhgOUQA7pziCVIcKIx7tDUG0TkGQCvBPCHIvJR7/PzInIfABhj2gDeBuCjAB4G8EFjzBe9Q7wbwGtE5FEoR9i7j/o3JEgwKRhrOqcx5l4A9wZ8/hyAu53/7wNwqIeUMWYV2uWiV9zTx3fGgWScw8VxGGffYzyVhH4JEpxEHIc1c4IECWLgVAjzoGmjR4W46aki8oSIfEFEPjuI97PHsUVeG1H8irf98yJy51GMq49x3iUim961+6yIvHMMY3y/iCyFhUf7vpbGmBP/AvBiaPzufgCXQvZJA7gC7f+cBfA5AC854nG+B8A7vPfvAPDzIfs9AeDMEY6r67WB+jg+As0LeAWAPxvDfY4zzrsAfHhcz6I3hm8EcCeAh0K293UtT4VmNoOnjR4VRpKeOgTEuTavB/CbRvEAgBkv9j9p4xw7jDGfAhDFztbXtTwVwhwTUWmjR4W46akGwMdE5EEvs23UiHNtJuH6xR3DK0XkcyLyERF56dEMrSf0dS1PDNPIpKSNdj1JdIvbuHiVMeY5r5/1x0XkS95sPyrEuTZHcv26IM4YPgPgJmNMXUTuBvD7AC6OfGS9oa9reWKE2Yw2bXRoiBpn3Ba3RuPwMMYsici9UPNylMIc59ocyfXrgq5jMMZsOe/vE5FfE5EzxphJytnu61omZrZFVNroUaFreqqIlESkwvcAvg09tLLtE3GuzYcAvNnzxL4CwKax7XaPCl3HKSLnRLS4VUS+ASoDq0c8zm7o71qO06t3hN7DN0Bnu10A1wB81Pv8PID7fF7ER6Ae0Z8ewzjnoSQLj3p/5/zjhHpqP+e9vnhU4wy6NgB+FMCPeu8FSiJxBcAXEBI1mIBxvs27bp8D8ACAvzSGMf42gOcB7HnP5Q8N41omGWAJEpwQJGZ2ggQnBIkwJ0hwQpAIc4IEJwSJMCdIcEKQCHOCBCcEiTAnSHBCkAhzggQnBIkwJ+gbInJRRO4Xkcsi8h4ReWzcYzrNSIQ5QV/w2gb9JoAfN0pfW4BmViUYE05MoUWCI8d3APhzY8xnvP8fBrAxxvGceiSaOUG/+IsAPuv8fzs03znBmJAIc4J+sQrgRQAgIi8H8GYAnx/riE45kkKLBH1BRM4A+EMARSin+fcBuNEYczDWgZ1iJMKcYGCIyAUA/8MY8/Jxj+U0IzGzEwwDtyMxsceORDMnSHBCkGjmBAlOCBJhTpDghCAR5gQJTggSYU6Q4IQgEeYECU4IEmFOkOCEIBHmBAlOCBJhTpDghOD/AzeXY9M9apIlAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot the forced LNN's trajectories with random ICs\n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "color = ['orange', 'blue']\n",
    "for i in range(len(X0)):\n",
    "    ax.plot(traj[:,i,0], traj[:,i,1], color='blue', alpha=0.1);\n",
    "ax.set_xlim([-1,1])\n",
    "ax.set_ylim([-1,1])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"LNN's learned trajectories\")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0.5, 1.0, 'Learned Lagrangian & Vector Field')"
      ]
     },
     "execution_count": 36,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 216x216 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Plot Lagrangian and learned vector field\n",
    "n_grid =  50\n",
    "x = torch.linspace(-1,1,n_grid)\n",
    "Q, P = torch.meshgrid(x,x)\n",
    "H, U, V = torch.zeros(Q.shape), torch.zeros(Q.shape), torch.zeros(Q.shape)\n",
    "for i in range(n_grid):\n",
    "    for j in range(n_grid):\n",
    "        x = torch.cat([Q[i,j].reshape(1,1),P[i,j].reshape(1,1)],1).to(device)\n",
    "        H[i,j] = model.defunc.m.L(x).detach().cpu()\n",
    "        O = model.defunc(0,x).detach().cpu()\n",
    "        U[i,j], V[i,j] = O[0,0], O[0,1]\n",
    "        \n",
    "fig = plt.figure(figsize=(3,3))\n",
    "ax = fig.add_subplot(111)\n",
    "ax.contourf(Q,P,H,100,cmap='RdYlBu')\n",
    "ax.streamplot(Q.T.numpy(),P.T.numpy(),U.T.numpy(),V.T.numpy(), color='black')\n",
    "ax.set_xlim([Q.min(),Q.max()])\n",
    "ax.set_ylim([P.min(),P.max()])\n",
    "ax.set_xlabel(r\"$q$\")\n",
    "ax.set_ylabel(r\"$p$\")\n",
    "ax.set_title(\"Learned Lagrangian & Vector Field\")"
   ]
  }
 ],
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